Problem
I am given a continuous and differentiable* function $f: \mathbb{R}^n \rightarrow \mathbb{R}^m$, where $m$ and $n$ are integers bigger than 1.
Is there a way to choose a set of input vectors such that the corresponding function outputs are uniformly distributed? Or, can we reduce the problem to some well studied problem for which polynomial time approximation algorithms may exist?
Remarks
* I'm measuring the distances in $\mathbb{R}^n$ and $\mathbb{R}^m$ using euclidean distance, but that's not a strict requirement.
** Similarly, I could also solve my (actual, practical) problem if there was a way to choose a the function inputs s.t. no two of the corresponding outputs have a distance smaller than some constant, predefined $\alpha$.
*** The input domain is constrained, s.t. for any input $x = <x_1, x_2, ..., x_n>$ we have $c_{lower} < x_i < c_{upper} $ for $i \in \{1,...,n\}$, where $c_{lower} \in \mathbb{R}$ and $c_{upper} \in \mathbb{R}$ are constants.